An implicit pseudo‐spectral multi‐domain method for the simulation of incompressible flows

Abstract

SUMMARYA pseudo-spectral method for the solution of incompressible ow problems based on an iterative solver involving an implicit treatment of linearized convective terms is presented. The method allows the treatment of moderately complex geometries by means of a multi-domain approach and it is able to cope with non-constant uid properties and non-orthogonal problem domains. In addition, the fully implicit scheme yields improved stability properties as opposed to semi-implicit schemes commonly employed. Key components of the method are a Chebyshev collocation discretization, a special pressure-correction scheme, and a restarted GMRES method with a preconditioner derived from a fast direct solver. The performance of the proposed method is investigated by considering several numerical examples of di erent complexity, and also includes comparisons to alternative solution approaches based on ÿnite-volume discretizations.

A multigrid pseudo-spectral method for incompressible Navier–Stokes flows

“…The linear systems on the different grid levels are obtained by applying the pseudo-spectral scheme as described above on the corresponding grids. The formation of the system matrices in (10) is made using the representation (6) together with the linearization technique (5) and a boundary conditions in the following way:…”

“…The present work tries to combine the advantages of spectral discretizations and multigrid solvers. The underlying spectral approach consists in the Chebyshev pseudo-spectral method presented in details in [10,11]. The involvement of a multigrid procedure aims to further increase the computational efficiency of this scheme.…”